To determine the domain of the function [tex]\( y = \sqrt{x} \)[/tex], we need to identify all the possible values of [tex]\( x \)[/tex] for which the function is defined. The domain of a function is the set of all permissible input values (i.e., values of [tex]\( x \)[/tex]).
1. The function [tex]\( \sqrt{x} \)[/tex] involves a square root.
2. For real numbers, the square root function [tex]\( \sqrt{x} \)[/tex] is only defined when [tex]\( x \)[/tex] is non-negative because the square root of a negative number is not a real number.
3. This implies that [tex]\( x \)[/tex] must be greater than or equal to 0.
Given these points, we conclude:
- [tex]\( x \)[/tex] cannot be negative because the square root of a negative number is not defined in the set of real numbers.
- [tex]\( x \)[/tex] can be zero or any positive number.
Thus, the domain of [tex]\( y = \sqrt{x} \)[/tex] is all [tex]\( x \)[/tex] such that [tex]\( x \)[/tex] is greater than or equal to 0.
In mathematical notation, this is expressed as [tex]\( 0 \leq x < \infty \)[/tex].
Therefore, the correct choice among the options provided is:
[tex]\[ \boxed{0 \leq x < \infty} \][/tex]
This corresponds to option 3.
